Prices fell at an annual rate of 5.4%, compared with a 4.7% annual drop in May.
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In recent months, prices have been falling at rates not seen since the early 1930s. Compared with May, prices dropped by 0.3%.
Summer sales meant clothing and footwear prices dropped by 2.6% in the month.
Mortgage repayments fell again as more ECB interest rate cuts were passed on to homeowners.
Food prices were also lower, but transport costs rose 1.5% as petrol and diesel prices increased.
A breakdown showed that prices of goods dropped by 5% in the year to June, while services showed a fall of 5.6%.
Clothing and footwear prices have fallen by more than 12% over the year, while housing, water, electricity, gas and other fuels - the category which includes mortgage repayments - are down 25.6%.
